1. Field of the Invention
The present invention relates to wheel inspection technology for a vehicle, and particularly, to a method and apparatus for tuning a parameter of a Kalman filter in a wheel inspection to remove noises in wheel inspection data more effectively.
2. Description of Related Art
For railway vehicles, especially for high speed railway vehicles, wheels are very important and costive assets. Generally, each wheel costs about $10,000, and a rolling stock has about 100 wheels. Given this, the cost of the wheels in one vehicle is very high. In addition, the wheels directly impact the vehicle's speed, safety and comfort.
To minimize wheel failure and to avoid catastrophic events, railway operators are usually equipped with a wheel inspection system to monitor relevant parameters of the wheels and to detect abnormal conditions of the wheels. In the existing wheel inspection systems, usually sensors are installed on the rail and are used to measure the relevant parameters of the wheels. This wheel data is then provided to a status inspection system to analyze whether the shape of the wheel is circular, whether the wheel is worn down, what the wheel diameter difference is, etc., to help the operators know the status of the wheels. In general, the detected relevant parameters of the wheel include a wheel profile and wheel diameter value.
It is well known that there exists noise in the wheel data measured by the sensors, which would cause an error in the analysis result of the wheel data, and may make the analysis result meaningless or generate false alarms. Therefore, it is necessary to remove the noise in the wheel inspection data to ensure that the analysis result can indicate the current status of the wheels accurately. Thus, Kalman filtering technology is often effectively used in the existing wheel inspection system to remove the noise in the signals.
The basic idea of the Kalman filter is to calculate an estimation value of the current status based on the estimation value of the previous status and the measurement value of the current status—It is a kind of recursive estimation. The operation of the Kalman filter includes two phases: prediction and update. In the prediction phase, the current status is predicted based on the estimation value of the previous status. In the update phase, the prediction value obtained in the prediction phase is optimized based on the measurement value of the current status to obtain the more accurate new estimation value.
In the prediction phase, the current status is predicted under formula (1):{circumflex over (x)}k−=Axk−1  (1)
where {circumflex over (x)}k− represents the status prediction value for time k, A represents a status transition matrix, and xk−1 represents the status estimation value for time k−1. Thus the prediction value of the prediction estimation covariance for time k is:Pk−=APk−1AT+Q  (2)
where Pk− represents the prediction value of the prediction estimation covariance for time k and Pk−1 represents the estimation value of the prediction estimation covariance for time k−1.
In the update phase, Kalman gain is calculated from formula (3):Kk=Pk−(Pk−+R)−1  (3)
where Kk represents the gain for time k, and R represents the measurement error covariance and is a constant. Then, the status prediction value for time k is updated under formula (4) to obtain the new status estimation value:{circumflex over (x)}k={circumflex over (x)}k−+Kk(zk−{circumflex over (x)}k−)  (4)
where {circumflex over (x)}k represents the status estimation value for time k, and zk represents the status measurement value for time k. In addition, the prediction value of the prediction estimation covariance is updated under formula (5) to obtain the new estimation value of the prediction estimation covariance:Pk=(I−Kk)Pk−  (5)
where Pk represents the estimation value of the prediction estimation covariance for time k.
In the Kalman filter, the Kalman gain Kk is in fact a balance factor for the prediction estimation covariance Pk and the measurement error covariance R. If the measurement error covariance R is close to 0, the Kalman gain Kk is close to 1, and the updated status estimation value {circumflex over (x)}k is close to the status measurement value zk. If the prediction estimation covariance Pk is close to 0, the Kalman gain Kk is also close to 0, and the updated status estimation value {circumflex over (x)}k is close to the status prediction value {circumflex over (x)}k−.
In the use of the Kalman filter, the measurement error covariance R is usually unchanged. However, in practice, the measurement error covariance R cannot remain unchanged. For example, in the case that the weather condition is changed or the working time is long, the sensors installed on the rail will be affected, leading to the measurement error covariance R being changed. Once the parameter of the Kalman filter is inappropriate, the signal noise remove effect will be decreased, easily resulting in the wrong analysis result. Therefore, it is necessary to consider the changes of the measurement error covariance R of the Kalman filter in the wheel inspection to make the estimation result of the Kalman filter more accurate.